When the outcome affects the second outcome, which is what we called dependent events.

Dependent events: Two events are dependent when the outcome of the first event influences the outcome of the second event. The probability of two dependent events is the product of the probability of X and the probability of Y AFTER X occurs.

$$P(X \, and \, Y)=P(X)\cdot P(Y\: after\: x)$$

Example

What is the probability for you to choose two red cards in a deck of cards?

A deck of cards has 26 black and 26 red cards. The probability of choosing a red card randomly is:

Inclusive events are events that can happen at the same time. To find the probability of an inclusive event we first add the probabilities of the individual events and then subtract the probability of the two events happening at the same time.

Video lesson

At Ann's 7-years olds party all 20 invited guests are going to get some candy from the fish pond. In 12 of the bags there is an extra chocolate bar. Tina and James are first and second out, what is the probability that they both get a bag with an extra chocolate bar?